1
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Question

# The number of possible straight lines , passing through (2,3)and forming a triangle with coordinate axes, whose area is 12 sq. units is

A
one
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B
two
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C
three
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D
four
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Solution

## The correct option is D fourSince the coordinate axes form the two sides of the triangle required, the triangle is always a right angled triangle.If a and b are the x-intercept and y-intercept reapectively,then , 0.5ab=±12⇒ab=±24Thus the answer to the question is 4(+a,+b),(+a,−b),(−a,+b),(−a,−b)The equation of the line isxa+yb=1 and ab=24 . It passes through (2,3)2a+3a24=1Solving a=4 and b=6Thus the answer to the question is four .x4+y6=1x4−y6=1−x4+y6=1−x4−y6=1

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